How to replace mesh data in linked object by another object's linked data?
Select the object whose mesh you want to replace, then go to the "Object Data" tab in the properties panel (the one with the triangle standing on one of its vertices). The topmost dropdown menu lets you select the mesh linked to your object. Just select MeshData1 here.


The little number on the right also tells you how many users your mesh has (to how many objects it is linked).